Profitability of technical trading strategies under market manipulation

Most technical trading strategies use the official closing price for analysis. But what is the effect when the official closing price is subject to market manipulation? This paper answers this question by testing the difference of profitabilities between using the official closing price and the last tick price. The results show a significant improvement of profitability by using the last tick price over the official closing price based on a data set in Hong Kong from 2011 to 2018.

, and Kandel et al. (2012) study the France stock market; Kucukkocaoglu (2008) studies the Istanbul stock market; McInish and Wood (1990) study the Canada stock market; Hsieh (2015) studies the Taiwan stock market; Kandel et al. (2012) study the Italy stock market; Hagströmer and Nordén (2014) study the Sweden stock market. The day-end effect on the closing price is far from an area-specific problem.
The evidence of closing price manipulation is the systematic price movement near the market close. This anomaly potentially affects everything that relies on the closing price, including return calculation and valuation. Stock exchanges over the world seek a solution to prevent closing price manipulation. Many exchanges introduce closing call auctions to determine the closing price to decrease the chance of manipulation. Comerton-Forde and Rydge (2006) investigate various algorithm designs for call auctions. They find that some algorithm designs of call auction systems can prevent manipulation. Empirically, Comerton-Forde et al. (2007), Pinfold and He (2012), Hagströmer and Nordén (2014), Huang and Chan (2014), and Kadıoğlu et al. (2015) study the implementation of closing call auction in different regions. The results mainly show that closing call auction reduces manipulation. Most major exchanges adopt closing auction methodology to determine the closing price.
Additionally, Hillion and Suominen (2004) and Comerton-Forde and Putniņš (2011b) use theoretical model to study real stock manipulation cases to seek explanation for manipulation. Both models suggest strong incentives for market manipulation. With the rise of high-frequency trading possibly to exploit the opportunity, Aitken et al. (2015) find increases of manipulation in both frequency and severity. Comerton-Forde and Putniņš (2011a) and Comerton-Forde and Putniņš (2013) formulate frameworks for the measurement of manipulation in terms of frequency and severity. Bogousslavsky and Muravyev (2020) study order imbalances at the close and find that order imbalances potentially can distort closing prices.
The main goal of this study is to investigate the impact of closing price manipulation from a practical point of view. As an illustration, there is no manipulation, and the closing price is "clean" in a perfect world. In an imperfect world, there is manipulation, and the closing price is "dirty". Between the two worlds lies the real world, where closing price methodology is designed to find the official closing price as shown in Fig. 1. Whereas the official closing price is the default choice for most financial purposes, there are flexible applications. In technical analysis, the closing price is an essential input. If the official closing price is still subject to market manipulation after the closing auction methodology, what is the impact on profitability? Brock et al. (1992) present a seminal empirical work on the profitability of technical analysis. The methodology adopted in this study is based on an extension of their work [see for example Chan et al. (2016)] where the objective is to show the impact on profitability in different situations.

Methodology
In this study, a collection of technical trading strategies is selected from the literature. They are characterized by different parameters, but all strategies need to have the closing price as their input to compute the trading signals. Based on the trading signals, the profitability of each technical trading strategy can then be computed. Instead of using the closing price, the same numerical experiment is repeated with its substitute. The difference between the two computed profitabilities is then tested statistically.
For this study to make sense, the substitute of the official closing price should be chosen to reflect the stock's true value near the market close. Otherwise, feeding random prices to quantitative trading strategies definitely can significantly change profitability, but the conclusion is meaningless. In this study, the traded price of the very last tick recorded in the continuous trading session is used to substitute the official closing price to generate trading signals. There are two reasons. First, regardless of the closing price methodology, the official closing price is still subject to manipulation and thus may not reflect the true value. Second, the last tick price is not as widely used as the official closing price. It should not be subject to the same pressure of potential manipulation. Moreover, it is the traded price nearest market close. Summarily, the last tick price is another proxy of "clean" closing price in Fig. 1.
Following Chan et al. (2016), profitabilities of various representative technical trading strategies using the official closing price versus the last tick price is compared. The strategies include Variable Length Moving Average (VMA), Fixed Length Moving Average (FMA), Trading Range Break (TRB), Relative Strength Index (RSI), and Intraday and Interday Momentum (IIM) with their full description in "Appendix". There are 75 distinct strategies in total. The differences in profitabilities are then tested using Analysis of Variance (ANOVA) models with blocking.

Data description
The dataset covers the Hang Seng Index (HSI) constituents from 2011 to 2018 inclusively. The stock list excludes all infrequently traded stocks and captures high market capitalization. The official closing prices are collected from Bloomberg. The intraday data are collected from Hong Kong Exchanges and Clearing Limited (HKEx). There are 37 stocks with complete data, and their details are listed in Table 1.
HKEx has changed the trading hours of the stock market twice throughout the period. On March 7, 2011, they changed the lunch hour's break from 2 h to 1.5 h. On March 5, 2012, they further changed to 1 h. In addition to the lunch break, HKEx introduced Closing Auction Session in the Hong Kong stock market on July 25, 2016. The Closing Auction Session is a trading mechanism that allows trades to be executed at the closing price. Before introducing the auction mechanism, the closing price is the 15-second average price in the last minute of the trading day. The statistical tests include these two blocking factors.

Statistical results
The following one-way ANOVA model decomposes the differences in daily returns.
All blocks are specified in capital letters, and α i denotes the variables concerned: using the official closing price or the last tick price. Table 2 describes all the other blocking factors in the ANOVA. The observed variable is the daily return of the trading strategy on a particular trading day. The function aov in R gives the results in Table 3. Table 4 shows that using the last tick price increases profitability by 76 basis points a year ( 3.059300e −05 × 250 ) compared with the use of the official closing price as inputs for technical trading strategies to compute trading signals. The difference is both statistically and economically significant. The result is also consistent across different blocking factors including the lunch hours, closing price methodologies, calendar month/year, trading strategies, and stocks. In other words, while deciding on strategies, stocks, and time to apply technical analysis makes (1) r i,j,k,l,m,n,h =µ + α i + LUNCH j + CLOSING k , +MONTH l + YEAR m + STRATEGY n + STOCK h + ǫ i,j,k,l,m,n,h .  significant differences in performance, using last tick price to compute trading signals robustly improve the performance.

Discussion
The implications of the result are two-fold-both practical and theoretical. From a practical point of view, it suggests that the use of official closing price as inputs for quantitative trading strategies may not be optimal. Particularly, using the last tick price for technical analysis improves profitability. Nevertheless, the result suggests that the last tick price is the best proxy for the "clean" closing price. From a theoretical point of view, quantitative analysis of financial data should yield useful results. Under the garbage-in-garbage-out principle, better inputs for the analysis should yield better results. When results are measured by profitability, the input showing higher profitability should be a better proxy to the "clean" closing price. In other words, this study also supports the argument that the last tick price is better than the official closing price to reflect the true market condition, possibly owing to closing price market manipulation. This result is surprising because literature generally suggests that closing price methodology such as closing call auction effectively reduces market manipulation. However, market manipulation is an adaptive process. As long as the official

Conclusion
This study investigates the sensitivity of profitability by altering the choice of input for trading strategies based on technical analysis. Statistical results show that using the last tick price increases the profitability significantly compared to the use of the official closing price in the Hong Kong stock market. Market manipulation may affect quantitative trading strategies, and it is worthwhile to search for better inputs for quantitative trading strategies.
Directions for future studies include a similar analysis on other markets, other periods, and other stocks, including less frequently traded stocks, to draw a broader conclusion. Finally, analytical models for this area are also important to address closing price manipulation and other economic issues.

Variable length moving average (VMA)
The VMA rule generates a signal by comparing the short moving average (SMA) and long-moving average (LMA). Given a band as a requirement, if the SMA is higher (lower) than the LMA more than the band, it generates a buy (sell) signal. Following Chan et al. (2016), this study includes 1-50, 1-150, 5-150, 1-200, 2-200 (period of SMAperiod of LMA) in our study.

Fixed length moving average (FMA)
The FMA strategy has a buy (sell) signal when the SMA crosses the LMA as follows: (above). Similarly, with the band as a requirement, the difference between LMA and SMA should be larger than the band to secure a signal. The holding period will be fixed as ten days according to Bessembinder and Chan (1998).

Trading range break (TRB)
The TRB strategy generates a signal if the stock price rises above the resistance (buy) or below the support level (sell). The resistance level is defined as follows: local maximum over n trading days where the support level is the minimum over n trading days. Similar to the FMA strategy, the holding period will be fixed as ten days according to Brock et al. (1992).

Relative strength index (RSI)
The RSI strategy using "50 crossover" trading rule is proposed by Wong et al. (2003). Let C t as the daily closing price at time t. First Step, we define U i = max(C i − C i−1 , 0) and D i = max(C i−1 − C i , 0) . Next, we compute U N (t) = 1 N t i=t−N +1 U i and D N (t) = 1 N t i=t−N +1 D i . Finally, the RSI at time t is defined as as follows.